Related papers: Discrete Vector-Valued Nonuniform Gabor Frames
Gabardo and Nashed have studied nonuniform wavelets based on the theory of spectral pairs for which the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum…
Deep Gaussian processes (DGPs) are popular surrogate models for complex nonstationary computer experiments. DGPs use one or more latent Gaussian processes (GPs) to warp the input space into a plausibly stationary regime, then use typical GP…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
Parseval frames can be thought of as redundant or linearly dependent coordinate systems for Hilbert spaces, and have important applications in such areas as signal processing, data compression, and sampling theory. We extend the notion of a…
Clinical time series are often irregularly sampled, with varying sensor frequencies, missing observations, and misaligned timestamps. Prior approaches typically address these irregularities by interpolating data into regular sequences,…
The Gradient Vector Flow (GVF) is a vector diffusion approach based on Partial Differential Equations (PDEs). This method has been applied together with snake models for boundary extraction medical images segmentation. The key idea is to…
We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear.…
Recent works have established a novel viewpoint that treats the eigenvalue spectra of disordered quantum systems as time-series, and corresponding algorithms such as singular-value-decomposition has proven its advantage in studying subtle…
Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…
Identifying causal relations among multi-variate time series is one of the most important elements towards understanding the complex mechanisms underlying the dynamic system. It provides critical tools for forecasting, simulations and…
A Wilson system is a collection of finite linear combinations of time frequency shifts of a square integrable function. In this paper we use the fact that a Wilson system is a shift-invariant system to explore its relationship with Gabor…
Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…
We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as $ \hat g(\xi)= \prod_{j=1}^n (1+2\pi i\delta_j\xi)^{-1}…
Our digital world is full of time series and graphs which capture the various aspects of many complex systems. Traditionally, there are respective methods in processing these two different types of data, e.g., Recurrent Neural Network (RNN)…
The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…
The concept of weaving of frames for Hilbert spaces was introduced by Bemrose et al. in 2016. Two frames $\{f_k\}_{k\in I}, \{g_k\}_{k\in I}$ are woven if the ``mixed system" $\{f_k\}_{k\in \sigma} \cup \{g_k\}_{k\in I\setminus \sigma}$ is…
The article describes a system for image recognition using deep convolutional neural networks. Modified network architecture is proposed that focuses on improving convergence and reducing training complexity. The filters in the first layer…
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
We define the framed DDF operators by introducing the concept of local frames in the usual formulation of DDF operators. In doing so it is possible to completely decouple the DDF operators from the associated tachyon and show that they are…